The fan will work better when it's pulling air instead of pushing it. Best place for it would be near the vent into the attic, or better yet, in the attic itself. This should help with temps and humidity a little. A carbon filter will work great for the smell if you can get the humidity down. Just be sure to get one that is rated for your fan. You can mount it before your hood so the airflow goes like this:

Carbon filter >>> Hood >>> Inline exhaust >>> Attic

Also the less bends in your ducts, the better your fan will work.